It is well known that mechanical disturbances can be used to establish elastic waves in earth formations surrounding a borehole, and the properties of these waves can be measured to obtain important information about the formations through which the waves have propagated. Parameters of compressional, shear and Stoneley waves can be indicators of formation characteristics. In particular, wave velocity (or its reciprocal, slowness) helps in evaluation of the location and/or producibility of hydrocarbon resources.
One example of a logging device that has been used to obtain and analyze acoustic measurements of formations surrounding an earth borehole is a Dipole Shear Sonic Imager (“DSI”—trademark of Schlumberger), and is of the general type described in Harrison et al., “Acquisition and Analysis of Sonic Waveforms From a Borehole Monopole And Dipole Source For The Determination Of Compressional And Shear Speeds And Their Relation To Rock Mechanical Properties And Surface Seismic Data,” Society of Petroleum Engineers, SPE 20557, 1990. According to conventional use of the DSI logging tool, one can present compressional slowness, Δtc, shear slowness, Δts, and Stoneley slowness, Δtst, each as a function of depth, z (slowness corresponds to an interval wave transit time typically measured by sonic logging tools).
An acoustic source in a fluid-filled borehole generates headwaves, as well as relatively stronger borehole-guided modes. A standard sonic measurement system includes a piezoelectric source and hydrophone receivers inside a fluid-filled borehole. The piezoelectric source may be either a monopole or a dipole source. The source bandwidth typically ranges from a 0.5 to 20 kHz. A monopole source primarily generates the lowest-order axisymmetric mode, also referred to as the Stoneley mode, along with compressional and shear headwaves. In contrast, a dipole source primarily excites the lowest-order flexural borehole mode together with compressional and shear headwaves. The headwaves are caused by the coupling of the transmitted acoustic energy to plane waves in the formation that propagate along the borehole axis. An incident compressional wave in the borehole fluid produces critically refracted compressional waves in the formation. The waves refracted along the borehole surface are known as compressional headwaves. The critical incidence angle is represented as θi=sin−1(Vf/Vc), where Vf is the compressional wave speed through the borehole fluid and Vc is the compressional wave speed through the formation. As a compressional headwave travels along an interface, it radiates energy back into the fluid that can be detected by the hydrophone receivers placed in the fluid-filled borehole. In relatively fast formations, the shear headwave can be similarly excited by a compressional wave at the critical incidence angle θi=sin−1(Vf/Vs), where Vs is the shear wave speed through the formation. It is also worth noting that headwaves are excited only when the wavelength of the incident wave is smaller than the borehole diameter so that the boundary can be effectively treated as a planar interface. In a homogeneous and isotropic model of fast formations, as above noted, compressional and shear headwaves can be generated by a monopole source placed in a fluid-filled borehole to determine the formation compressional and shear wave speeds. However, refracted shear headwaves cannot be detected for slow formations (where the shear wave velocity is less than the borehole-fluid compressional wave velocity) with receivers placed in the borehole fluid. Therefore, formation shear velocities are obtained from the low-frequency asymptote of flexural dispersion for slow formations. There are standard processing techniques for the estimation of formation shear velocities in either fast or slow formations from an array of recorded dipole waveforms.
Both the monopole and dipole waveforms recorded at an array of receivers can be processed by a modified matrix pencil algorithm that isolates non-dispersive and dispersive arrivals in the wave train. The compressional headwave velocity is the formation quasi-compressional qP−) wave velocity along the borehole axis. The zero-frequency intercept of the lowest-order axisymmetric Stoneley dispersion yields the tube wave velocity (VT) along the borehole axis. The formation quasi-shear (qSV−) and shear (SH−) velocities are obtained from the low-frequency asymptotes of the two orthogonally polarized borehole flexural waves propagating along the borehole axis.
Among the areas of interest of the present invention is the field of seismic prospecting. Seismic prospecting for hydrocarbon reserves requires estimates of all the five transversely isotropic (TI−) anisotropic constants of overburden shale for reliable identification and location of target reservoirs. Shale typically constitutes more than 70% of the formation that a borehole trajectory passes through before reaching the target reservoir. Consequently, if the proper anisotropic constants of shale are not accounted for in the velocity model, it is more probable that drilling based on seismic prospecting will miss the target reservoir.
Sedimentary rocks frequently possess an anisotropic structure resulting, for example, from thin bedding, fine scale layering, the presence of oriented microcracks or fractures, or the preferred orientation of nonspherical grains or anisotropic minerals. This type of anisotropy is called formation intrinsic anisotropy. A dipole dispersion crossover is an indicator of stress-induced anisotropy dominating any intrinsic anisotropy that may also be present.
Failure to properly account for anisotropy in seismic processing may lead to errors in velocity analysis, normal moveout (NMO) correction, dip moveout (DMO) correction, migration, time-to-depth conversion and amplitude versus offset (AVO) analysis. The main cause of anisotropy in sedimentary basins is the presence of shales which, as noted above, typically form a major component of the basin, and overlie many hydrocarbon reservoirs. Shales are anisotropic as a result of layering and a partial alignment of plate-like clay minerals. This anisotropy may be described, to a good approximation, as being transversely isotropic (TI). A TI medium is invariant with respect to rotations about a symmetry axis and may be described by five independent elastic stiffnesses. An example is a sedimentary rock for which the bedding plane is a plane of isotropy.
AVO analysis requires some combinations of formation anisotropic constants. Some of these constants can be obtained from the borehole sonic measurements, others can be obtained from borehole seismic measurements, such as walk-away vertical seismic profiles (VSPs). The elastic constants that can be obtained from the borehole sonic measurements are the three formation shear moduli and a compressional modulus from the compressional headwave logging.
Two of the shear moduli, known to those of skill in the art as c44 and c55, can be obtained from the fast and slow dipole flexural dispersions. A recently issued patent (U.S. Pat. No. 6,611,761 entitled “Sonic Well Logging for Radial Profiling,” hereby incorporated by reference) describes a technique for obtaining radial profiles of fast and slow shear slownesses using measured dipole dispersions in two orthogonal directions that are characterized by the shear moduli c44 and c55 for a borehole parallel to an X3-axis (FIG. 1) in an orthorhombic formation. However, the third shear modulus, known as c66, is different. The third shear modulus can be estimated from tube wave velocity. The tube wave velocity is the zero-frequency intercept of borehole Stoneley dispersion.
Typical logging devices such as the DSI are generally quite flexible and therefore approximately “acoustically transparent.” The advantage of typical flexible logging devices is the acoustic transparency, which allows any signal propagation through the tool to be ignored. Accordingly, typical sonic data is collected and processed independent of tool effects. However, the drawback of flexible logging devices is mechanical weakness. In difficult logging conditions, flexible logging devices may buckle or otherwise fail. Stronger tools may be useful for difficult logging conditions, but stronger logging tools affect the acoustic signals, and current logging procedures ignore any tool influence.
A U.S. Pat. No. 6,714,480, issued Mar. 30, 2004 and entitled “Determination of anisotropic moduli of earth formations” (hereby incorporated by reference) describes a technique for estimating the horizontal shear modulus c66 of an orthorhombic or TI-formation using a zero frequency intercept of the Stoneley dispersion that yields tube wave velocity. This technique assumes that the borehole Stoneley dispersion is insignificantly affected by the presence of the sonic tool structure or any possible near-wellbore alteration, such as super-charging in a permeable formation, and shale swelling in overburden shales. Nevertheless, new observations reveal that especially in fast formations and small borehole diameters, both sonic tool effects and near-wellbore alteration can have significant effects on the measured Stoneley dispersion and cause a significant bias on the estimate of the horizontal shear modulus c66.